Reconstruction of multiplicative space- and time-dependent sources

This paper presents a numerical regularization approach to the simultaneous determination of multiplicative space- and time-dependent source functions in a nonlinear inverse heat conduction problem with homogeneous Neumann boundary conditions together with specified interior and final time temperature measurements. Under these conditions a unique solution is known to exist. However, the inverse prob- lem is still ill-posed since small errors in the input interior temperature data cause large errors in the output heat source solution. For the numerical discretisation, the boundary element method combined with a regularized nonlinear optimization are utilized. Results obtained from several numerical tests are provided in order to illustrate the efficiency of the adopted computational methodology

Transmutation operators as a solvability concept of abstract singular equations

One of the methods of studying differential equations is the transmutation operators method. Detailed study of the theory of transmutation operators with applications may be found in the literature. Application of transmutation operators establishes many important results for different classes of differential equations including singular equations with Bessel operato

Variational iteration method for inverse problem of diffusion equation

WOS: 000285931900017In this work, the solution of an inverse problem concerning a diffusion equation with source control parameters is presented. Inverse problems of parabolic type arise from many fields of physics and play a very important role in various branches of science and engineering. In the last few years, considerable efforts have been expended in formulating accurate and efficient methods to solve these equations. In this research, the variational iteration method is used for solving an inverse parabolic problem and computing an unknown time-dependent parameter. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or perturbation theory. The results show applicability, accuracy and efficiency of VIM in solving inverse problems of parabolic type. It is predicted that VIM can be widely applied in science and engineering problems. Copyright (C) 2009 John Wiley & Sons, Ltd